Figure 1.

Summary of statistical methods used by the working group on collapsing methods. The methods are organized into four broad categories: (1) early-developed burden tests based on linear statistics, (2) well-established variance-components-type tests based on quadratic statistics, (3) recently developed hybrid methods that combine burden and nonburden tests, and (4) other methods based on dimension-reduction techniques. The burden tests use linear weights to compute a weighted-sum statistic representing all rare variants in a region. These early tests are unidirectional by construction, assuming that all variants affect the phenotype in the same direction. The well-established variance-components-type tests use quadratic statistics for rare variants. These methods make no assumption on the direction of the effect on phenotype and therefore are able to handle both at-risk and protective variants. Both the recently developed hybrid methods and the other methods based on dimension-reduction techniques are also bidirectional approaches. CAST, cohort allelic sum test; CMC, combined multivariate and collapsing; PCA, principal components analysis; RBS, replication-based weighted-sum statistic; SKAT, sequence kernel association test; SKAT-O, SKAT with the use of the optimal weighted average; SST, simple sum test; VT, variable-threshold; w-SUM, group-wise weighted sum.